## S4 class stanmodel 'DE-modelSpec' coded as follows:
## data {
## int<lower=0> N; // num observations
## int<lower=0> ni; // num items
## int<lower=0> ns; // num subjects
## int<lower=0> nsi; // num subject-item combos
## int<lower=0> si_lookup[ns, ni]; // lookup table for sparsely coded subject-item offsets
## int<lower=0> nt; // num trials
## int<lower=0> nc; // num strategies
## real<lower=0> y[N]; // log RT
## int<lower=0> strategy[N]; // strategy for a given obs
## int<lower=0> item[N]; // item for a given obs
## int<lower=0> subject[N]; // subject for a given obs
## int<lower=0> trial[N]; // trial for a given obs
## }
##
## parameters {
## real A; // = log_A, to be exponentialted later
## real A_es[ns];
## real A_ei[ni];
## //real A_esi[ns,ni];
## real A_esi[nsi];
## real<lower=0> sigma_A_ei;
## real<lower=0> sigma_A_es;
## real<lower=0> sigma_A_esi;
##
## real B; // = log_B, to be exponentialted later
## real B_es[ns];
## real B_ei[ni];
## //real B_esi[ns,ni];
## real B_esi[nsi];
## real<lower=0> sigma_B_ei;
## real<lower=0> sigma_B_es;
## real<lower=0> sigma_B_esi;
##
## real T;
## real T_es[ns];
## real T_ei[ni];
## //real T_esi[ns,ni];
## real T_esi[nsi];
## real<lower=0> sigma_T_ei;
## real<lower=0> sigma_T_es;
## real<lower=0> sigma_T_esi;
##
## real R;
## real R_es[ns];
## real R_ei[ni];
## //real R_esi[ns,ni];
## real R_esi[nsi];
## real<lower=0> sigma_R_ei;
## real<lower=0> sigma_R_es;
## real<lower=0> sigma_R_esi;
##
## // add sigma variability
##
## real<lower=0> sigma;
## }
##
## transformed parameters {
## real y_hat[N];
## real Alpha;
## real Beta;// = B + B_es[subject[i]] + B_ei[item[i]] + B_esi[subject[i], item[i]];
## real log_Rate;// = R + R_es[subject[i]] + R_ei[item[i]] + R_esi[subject[i], item[i]];
## real log_Tau;// = T + T_es[subject[i]] + T_ei[item[i]] + T_esi[subject[i], item[i]];
##
## for(i in 1:N){
## Alpha = exp(A + A_es[subject[i]] + A_ei[item[i]] + A_esi[si_lookup[subject[i], item[i]]]);
## Beta = exp(B + B_es[subject[i]] + B_ei[item[i]] + B_esi[si_lookup[subject[i], item[i]]]);
## log_Rate = R + R_es[subject[i]] + R_ei[item[i]] + R_esi[si_lookup[subject[i], item[i]]];
## log_Tau = T + T_es[subject[i]] + T_ei[item[i]] + T_esi[si_lookup[subject[i], item[i]]];
## // Tau = exp(Tau*Rate)-2; // old transformed version
## // print(log_Alpha[i]);
## // print(log_Beta[i]);
## // print(Tau[i]);
## // print(Rate[i]);
## // print(exp(log_Alpha[i]) + exp(log_Beta[i]) * (Tau[i]+1) / (Tau[i] + trial[i]^Rate[i]));
## // print(log(exp(log_Alpha[i]) + exp(log_Beta[i]) * (Tau[i]+1) / (Tau[i] + trial[i]^Rate[i])));
## // print("");
## y_hat[i] = log(Alpha + Beta * (exp(log_Tau) + 1)/(exp(log_Tau) + exp(exp(log_Rate)*trial[i])));
## // this resulted in no delayed start ever... : log(exp(log_Alpha) + (exp(log_Beta) * (exp(log_Tau) + 1) /(exp(log_Tau) + exp(log_Rate)*trial[i])));
## // **old transformed version** log(exp(log_Alpha) + exp(log_Beta) * (Tau+1) / (Tau + trial[i]^Rate));
## // go back to original version, but constrain Tau, Rate to be positive
## }
## }
##
## model {
## sigma ~ exponential(.1);
##
## A ~ normal(0, 6); // set as overall mean and sd of data
## B ~ normal(8, 5); // set as mean, sd for retrieval trials
## T ~ normal(5, 10); // was centered on 0
## R ~ normal(-1, 2);
##
## sigma_A_es ~ exponential(1);
## sigma_A_ei ~ exponential(1);
## sigma_A_esi ~ exponential(1);
##
## sigma_B_es ~ exponential(1);
## sigma_B_ei ~ exponential(1);
## sigma_B_esi ~ exponential(1);
##
## sigma_R_es ~ exponential(1);
## sigma_R_ei ~ exponential(1);
## sigma_R_esi ~ exponential(1);
##
## sigma_T_es ~ exponential(1);
## sigma_T_ei ~ exponential(1);
## sigma_T_esi ~ exponential(1);
##
## A_es ~ normal(0, sigma_A_es);
## A_ei ~ normal(0, sigma_A_ei);
## A_esi ~ normal(0, sigma_A_esi);
## // for(i in 1:ns) {
## // for(j in 1:ni)
## // A_esi[i,j] ~ normal(0, sigma_A_esi);
## // }
##
## B_es ~ normal(0, sigma_B_es);
## B_ei ~ normal(0, sigma_B_ei);
## B_esi ~ normal(0, sigma_B_esi);
## // for(i in 1:ns) {
## // for(j in 1:ni)
## // B_esi[i,j] ~ normal(0, sigma_B_esi);
## // }
##
## R_es ~ normal(0, sigma_R_es);
## R_ei ~ normal(0, sigma_R_ei);
## R_esi ~ normal(0, sigma_R_esi);
## // for(i in 1:ns) {
## // for(j in 1:ni)
## // R_esi[i,j] ~ normal(0, sigma_R_esi);
## // }
##
## T_es ~ normal(0, sigma_T_es);
## T_ei ~ normal(0, sigma_T_ei);
## T_esi ~ normal(0, sigma_T_esi);
## // for(i in 1:ns) {
## // for(j in 1:ni)
## // T_esi[i,j] ~ normal(0, sigma_T_esi);
## // }
##
## y ~ normal(y_hat, sigma);
## }
## generated quantities {
## vector[N] logLik;
## for(n in 1:N){
## logLik[n] = normal_lpdf(y[n] | y_hat[n], sigma);
## }
## }
Each spike represents the R-hat value for a particular component parameter. Below, very high values are examined more closely.
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| Parameter | param | mean | se_mean | sd | 2.5% | 25% | 50% | 75% | 97.5% | n_eff | Rhat | Rhat.z |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Alpha | A_esi[178] | 0.1528006 | 0.0578721 | 0.1310679 | -0.1292053 | 0.0688531 | 0.1624331 | 0.2472850 | 0.3816242 | 5.129252 | 1.338995 | 2.953078 |
| Alpha | A_esi[213] | 0.1883704 | 0.0782230 | 0.1427972 | -0.1334271 | 0.1060492 | 0.2110088 | 0.2874058 | 0.4168864 | 3.332497 | 1.647783 | 6.260338 |
| Alpha | A_esi[27] | 0.0609863 | 0.0918136 | 0.1739487 | -0.2493913 | -0.0794928 | 0.0581416 | 0.2031400 | 0.3543799 | 3.589454 | 1.628272 | 6.051369 |
| Beta | B_es[13] | -0.1770123 | 0.0310945 | 0.0895481 | -0.3495303 | -0.2317515 | -0.1759894 | -0.1185680 | -0.0064319 | 8.293639 | 1.266047 | 2.171779 |
| Beta | B_es[15] | -0.1228044 | 0.0249546 | 0.1012218 | -0.2983781 | -0.1906058 | -0.1369978 | -0.0659538 | 0.1137506 | 16.453022 | 1.232229 | 1.809567 |
| Beta | B_es[30] | -0.1190415 | 0.0265075 | 0.0844687 | -0.2846279 | -0.1755116 | -0.1198513 | -0.0601198 | 0.0392172 | 10.154364 | 1.233612 | 1.824381 |
| Log Posterior | lp__ | 5370.5209983 | 84.7640565 | 176.2218952 | 5105.4142170 | 5242.4500740 | 5355.1086325 | 5479.2603044 | 5781.7119056 | 4.322114 | 2.100838 | 11.112754 |
| Rate | R_es[15] | 0.2299083 | 0.4408033 | 0.7935105 | -1.1259960 | -0.5412067 | 0.4019762 | 0.9387771 | 1.3635766 | 3.240527 | 1.930861 | 9.292230 |
| Rate | R_es[29] | 0.6544375 | 0.1491148 | 0.4046219 | -0.1990594 | 0.3281066 | 0.7592682 | 0.9243157 | 1.3836030 | 7.363043 | 1.470547 | 4.362063 |
| Rate | R_es[3] | 0.7291509 | 0.1059177 | 0.2908746 | 0.1920788 | 0.5404653 | 0.7058102 | 0.9159891 | 1.3472402 | 7.541793 | 1.346481 | 3.033264 |
| Rate | R_es[5] | -1.1304937 | 0.1657355 | 0.6672449 | -2.2166805 | -1.6264138 | -1.3129994 | -0.6138894 | 0.1657230 | 16.208381 | 1.250619 | 2.006537 |
| Rate | R_esi[109] | -0.0974086 | 0.1414697 | 0.2649148 | -0.5016366 | -0.3041247 | -0.1491588 | 0.0892327 | 0.5003235 | 3.506592 | 1.729870 | 7.139530 |
| Rate | R_esi[121] | -0.1338524 | 0.0727463 | 0.1976933 | -0.4577024 | -0.2628953 | -0.1635148 | -0.0373821 | 0.3571796 | 7.385198 | 1.315517 | 2.701619 |
| Rate | R_esi[13] | -0.1269262 | 0.0727528 | 0.1977566 | -0.4794831 | -0.2850213 | -0.1203227 | -0.0021226 | 0.2774594 | 7.388612 | 1.309825 | 2.640655 |
| Rate | R_esi[145] | -0.2902321 | 0.0893930 | 0.2366871 | -0.6910108 | -0.4693277 | -0.3109885 | -0.1377721 | 0.2389899 | 7.010392 | 1.364337 | 3.224501 |
| Rate | R_esi[178] | 0.3635148 | 0.1248837 | 0.2529031 | -0.1416398 | 0.1914777 | 0.3851694 | 0.5468294 | 0.8007838 | 4.101070 | 1.490434 | 4.575056 |
| Rate | R_esi[213] | -0.0239842 | 0.1997790 | 0.3448358 | -0.7047983 | -0.2834701 | 0.0555124 | 0.2384631 | 0.5108027 | 2.979376 | 1.796669 | 7.854972 |
| Rate | R_esi[27] | -0.3512084 | 0.0765492 | 0.1931216 | -0.6984287 | -0.4895754 | -0.3547326 | -0.2275097 | 0.0191313 | 6.364733 | 1.324413 | 2.796905 |
| Rate | R_esi[5] | -0.1301388 | 0.0521256 | 0.2592350 | -0.6618646 | -0.2976963 | -0.1314962 | 0.0469936 | 0.3528312 | 24.733501 | 1.239540 | 1.887870 |
| Rate | R_esi[8] | 0.2612065 | 0.2335212 | 0.5939500 | -0.6755302 | -0.2808781 | 0.3140437 | 0.7637026 | 1.2549159 | 6.469146 | 1.341625 | 2.981253 |
| Sigma | sigma_B_esi | 0.0305271 | 0.0076675 | 0.0151755 | 0.0073465 | 0.0187892 | 0.0263785 | 0.0416571 | 0.0628671 | 3.917179 | 1.918590 | 9.160799 |
| Sigma | sigma_T_ei | 0.4050245 | 0.0911716 | 0.3193876 | 0.0443615 | 0.1840105 | 0.3096348 | 0.5477224 | 1.2738183 | 12.272038 | 1.319134 | 2.740359 |
| Sigma | sigma_T_esi | 2.0678775 | 0.0688242 | 0.3002637 | 1.5137520 | 1.8670463 | 2.0553590 | 2.2708286 | 2.6418036 | 19.033734 | 1.247863 | 1.977015 |
| Tau | T | 23.8535473 | 2.1530226 | 3.9948446 | 16.0259324 | 21.2129774 | 23.3844121 | 27.2410927 | 30.6917108 | 3.442727 | 1.820588 | 8.111160 |
| Tau | T_es[1] | -20.4749820 | 2.1896434 | 4.0881503 | -27.0891333 | -24.1573974 | -20.5786560 | -17.1123726 | -12.8726208 | 3.485836 | 1.769170 | 7.560449 |
| Tau | T_es[11] | -20.4016708 | 2.3522768 | 4.5592827 | -27.5928285 | -24.3406129 | -20.0467053 | -17.3453876 | -11.8535056 | 3.756784 | 1.667245 | 6.468783 |
| Tau | T_es[12] | -0.6214949 | 2.2479174 | 6.3338921 | -15.1779521 | -4.6214803 | 0.0319130 | 3.8943624 | 9.5399011 | 7.939271 | 1.257164 | 2.076634 |
| Tau | T_es[13] | 21.6531526 | 3.6339156 | 12.2278786 | 0.6402405 | 13.7129719 | 20.9200230 | 27.1539909 | 52.3350859 | 11.322767 | 1.252643 | 2.028216 |
| Tau | T_es[15] | 2.5774934 | 7.5637385 | 15.9405076 | -21.2803307 | -11.9408669 | 1.5737435 | 15.1908961 | 29.9265677 | 4.441516 | 1.628849 | 6.057541 |
| Tau | T_es[20] | -15.8989340 | 1.7779317 | 6.2625115 | -26.1629093 | -20.9263004 | -16.0031559 | -11.9487682 | -2.3030194 | 12.407004 | 1.291724 | 2.446789 |
| Tau | T_es[24] | -27.1840065 | 2.9688276 | 7.0709213 | -43.7298344 | -31.4064699 | -24.9899136 | -22.1674132 | -16.7840537 | 5.672599 | 1.647359 | 6.255795 |
| Tau | T_es[26] | -15.1759179 | 1.9949027 | 7.4141247 | -26.6184711 | -20.6528700 | -15.3389129 | -12.2530876 | 2.5509217 | 13.812629 | 1.280523 | 2.326819 |
| Tau | T_es[28] | -19.8071586 | 2.1666361 | 4.1731653 | -26.4430990 | -23.4760275 | -19.7276313 | -16.6322347 | -11.7035234 | 3.709874 | 1.740413 | 7.252444 |
| Tau | T_es[29] | 14.9829372 | 6.2569257 | 15.0624283 | -11.3536500 | 3.9256568 | 14.3589683 | 23.7244701 | 45.7895308 | 5.795194 | 1.506951 | 4.751966 |
| Tau | T_es[3] | 24.3081403 | 4.4516776 | 11.6606364 | 5.9970220 | 15.2433278 | 23.0240959 | 33.9518306 | 48.1309724 | 6.861153 | 1.448437 | 4.125255 |
| Tau | T_es[30] | -15.6189553 | 2.2332361 | 4.7894186 | -23.6488082 | -19.4685196 | -15.4023624 | -12.4252651 | -5.6216652 | 4.599348 | 1.591956 | 5.662401 |
| Tau | T_es[4] | -17.6077361 | 1.8862021 | 4.5730241 | -25.0268070 | -21.3688885 | -17.8048811 | -14.1384636 | -8.4266948 | 5.878013 | 1.541530 | 5.122320 |
| Tau | T_es[5] | -11.0453403 | 3.6334025 | 10.1961349 | -23.4936406 | -18.8786125 | -14.1087767 | -5.6840119 | 12.7572096 | 7.874883 | 1.393800 | 3.540062 |
| Tau | T_es[6] | -12.3758259 | 2.2351473 | 5.1117202 | -21.2198507 | -16.2136392 | -12.1620077 | -9.0314097 | -2.2858427 | 5.230243 | 1.484762 | 4.514312 |
| Tau | T_es[7] | -17.9045159 | 2.2429018 | 4.3909176 | -25.6737977 | -21.6300124 | -17.4599784 | -14.5351956 | -9.9576163 | 3.832569 | 1.627479 | 6.042872 |
| Tau | T_es[8] | -10.4910888 | 1.9525864 | 4.9571072 | -19.2105983 | -13.8036909 | -10.8614252 | -7.8093746 | -0.4684246 | 6.445195 | 1.276945 | 2.288500 |
| Tau | T_es[9] | -17.1972930 | 2.0258440 | 4.2490178 | -25.5740827 | -20.3899276 | -16.7079521 | -14.4982015 | -8.4031933 | 4.399113 | 1.562417 | 5.346031 |